Snaps in My Story last for 24-hours before disappearing. You can customize who can see your story. Follow these steps in Snapchat.
- Tap on your profile icon in the top left corner of the screen.
- Tap on the three vertical dots right to My Story.
- You will see a pop-up, Tap on Story Settings.
- You will see three option, Tap on Custom.
- Tap on the People Names you want to block your story for.
- You are done.